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This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. Protection from annual flooding is correlated with increased cholera prevalence in Bangladesh: a zero-inflated regression analysis Environmental Health 2010, 9:13 doi:10.1186/1476-069X-9-13 Margaret Carrel ([email protected]) Paul Voss ([email protected]) Peter K. Streatfield ([email protected]) Mohammad Yunus ([email protected]) Michael Emch ([email protected]) ISSN 1476-069X Article type Research Submission date 30 November 2009 Acceptance date 22 March 2010 Publication date 22 March 2010 Article URL http://www.ehjournal.net/content/9/1/13 This peer-reviewed article was published immediately upon acceptance. It can be downloaded, printed and distributed freely for any purposes (see copyright notice below). Articles in Environmental Health are listed in PubMed and archived at PubMed Central. For information about publishing your research in Environmental Health or any BioMed Central journal, go to http://www.ehjournal.net/info/instructions/ For information about other BioMed Central publications go to http://www.biomedcentral.com/ Environmental Health © 2010 Carrel et al. , licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formattedPDF and full text (HTML) versions will be made available soon.

Protection from annual flooding is correlated with increased cholera prevalencein Bangladesh: a zero-inflated regression analysis

Environmental Health 2010, 9:13 doi:10.1186/1476-069X-9-13

Margaret Carrel ([email protected])Paul Voss ([email protected])

Peter K. Streatfield ([email protected])Mohammad Yunus ([email protected])Michael Emch ([email protected])

ISSN 1476-069X

Article type Research

Submission date 30 November 2009

Acceptance date 22 March 2010

Publication date 22 March 2010

Article URL http://www.ehjournal.net/content/9/1/13

This peer-reviewed article was published immediately upon acceptance. It can be downloaded,printed and distributed freely for any purposes (see copyright notice below).

Articles in Environmental Health are listed in PubMed and archived at PubMed Central.

For information about publishing your research in Environmental Health or any BioMed Centraljournal, go to

http://www.ehjournal.net/info/instructions/

For information about other BioMed Central publications go to

http://www.biomedcentral.com/

Environmental Health

© 2010 Carrel et al. , licensee BioMed Central Ltd.This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0),

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Protection from annual flooding is correlated with increased cholera

prevalence in Bangladesh: a zero-inflated regression analysis

Margaret Carrel1*

, Paul Voss2, Peter K. Streatfield

3, Mohammad Yunus

3, and Michael Emch

1

1 Department of Geography, CB3220, University of North Carolina-Chapel Hill, Chapel Hill,

NC, USA 27599

2 Odum Institute for Research in Social Science, CB3355, University of North Carolina-Chapel

Hill, Chapel Hill, NC, USA 27599

3 Health and Demographic Surveillance Unit, International Center for Diarrheal Disease

Research, Bangladesh, Mohakhali, Dhaka 1212, Bangladesh

*Corresponding author

Email addresses:

MC: [email protected]

PV: [email protected]

PKS: [email protected]

MY: [email protected]

ME: [email protected]

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Abstract

Background

Alteration of natural or historical aquatic flows can have unintended consequences for regions

where waterborne diseases are endemic and where the epidemiologic implications of such

change are poorly understood. The implementation of flood protection measures for a portion of

an intensely monitored population in Matlab, Bangladesh, allows us to examine whether cholera

outcomes respond positively or negatively to measures designed to control river flooding.

Methods

Using a zero inflated negative binomial model, we examine how selected covariates can

simultaneously account for household clusters reporting no cholera from those with positive

counts as well as distinguishing residential areas with low counts from areas with high cholera

counts. Our goal is to examine how residence within or outside a flood protected area interacts

with the probability of cholera presence and the effect of flood protection on the magnitude of

cholera prevalence.

Results

In Matlab, living in a household that is protected from annual monsoon flooding appears to have

no significant effect on whether the household experiences cholera, net of other covariates.

However, counter-intuitively, among households where cholera is reported, living within the

flood protected region significantly increases the number of cholera cases.

Conclusions

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The construction of dams or other water impoundment strategies for economic or social motives

can have profound and unanticipated consequences for waterborne disease. Our results indicate

that the construction of a flood control structure in rural Bangladesh is correlated with an

increase in cholera cases for residents protected from annual monsoon flooding. Such a finding

requires attention from both the health community and from governments and non-governmental

organizations involved in ongoing water management schemes.

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Background

Several empirical studies have examined the impact of water construction projects on

communicable disease rates. With the exception of onchocerciasis, whose vector habitat is fast

moving streams, the rates of nearly every disease whose host or vector depend on standing water

sources increase when water resource management programs are implemented by governments

or NGOs [1-8]. Hughes and Hunter (1970) argue that programs which alter the human

environment result in the formation of new ‘ecological contracts,’ contracts that typically have

hidden or unanticipated costs. As Sow et al. (2002) contend, “feasibility studies mainly

emphasize the economic benefits rather than the environmental and health hazards of water-

resources developments.” Even if public health is given consideration in the planning stages of

water resource projects, the true impact of changes to aquatic systems on human health may not

be known for decades. Directly comparing pre- and post-development health data provides the

clearest understanding of how changes in water supplies have affected the disease experience of

local populations [4].

Since the 1950s, flood control and water management have been central issues for the

Bangladeshi government (officially East Bengal prior to 1947 and East Pakistan from 1947 to

1971). Starting with the 20-year Water Master Plan in 1964, and continuing through today,

heavy emphasis was placed on the construction of embankments around the country [9]. Initially,

water management efforts were organizationally top-down; there was little or no public input on

decisions that had a very tangible effect on the daily lives of Bangladeshis. Water plans since

1999, however, have involved greater public participation and worked to address issues such as

gender equity, social justice and environmental awareness while still focusing primarily on

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increasing agricultural production [10]. Yet, there remains little consideration of the potential

implications of such infrastructure investment for disease.

Among the thousands of kilometers of embankments that have been constructed in

Bangladesh is the Meghna-Dhonagoda Irrigation Project (MDIP), built in 1988-1989 and located

in Matlab (Figure 1). The MDIP, completed between two particularly sizeable flood years for

Bangladesh, consists of a 60km ring embankment, irrigation and drainage canals, culverts,

bridges and two pumping stations [11]. Matlab is a rural region, located ~50km southeast of

Dhaka where the Ganges and Meghna rivers join to form the Lower Meghna (Figure 2).

Running from north to south through Matlab is the Dhonagoda River. The MDIP embankment

along the Dhonagoda divides Matlab into two parts, one which experiences the seasonal flooding

of the Dhonagoda and one which is typically protected. The protected area makes up about 40%

of Matlab’s 184km2 [2, 12].

The population of Matlab is over 200,000 persons, with a population density of

approximately 1000 persons per square kilometer [2]. The people of Matlab live within a

structure of baris, or patrilineal household groupings. Since 1966 the population of Matlab has

been under demographic and health surveillance by the International Centre for Diarrhoeal

Disease Research, Bangladesh (ICDDR,B). Each resident of Matlab is assigned an identification

code, as is their household, and twice a month each household is visited by a trained community

worker who records demographic information such as births, deaths, marriages and illnesses [3].

Health information about the population of Matlab is gathered both at ICDDR,B’s hospital and

by the community health workers who visit each bari. Surveillance data shows that diarrheal and

other infectious diseases are highly endemic to the population. One such disease, cholera, is

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highly correlated with annual flood events, with incidence peaking in September through

December at the end of the monsoon season [13, 14].

Thus, in Matlab there exists a unique opportunity to conduct a longitudinal analysis

comparing disease pre- and post-implementation of a flood control program. In the present

analysis we examine whether residence within the flood protected area of Matlab is associated

with increased or decreased cholera prevalence. Previous studies have described a positive

association between residence in the flood control area and cholera, but over much shorter time

periods [3, 12]. Analyzing two full decades of data for this area, including for years prior to the

implementation of flood control and years following, provides a strong and robust test regarding

the possibility of long-term implications for human health of flood control programs.

Methods

Data from ICDDR,B’s health and demographic surveillance system is joined to

geographic information in a Geographic Information System (GIS) for Matlab. From the

ICDDR,B health records, we have data on 8,500 laboratory-confirmed cholera cases between

January 1, 1983 and December 31, 2003. This 21 year time frame spans the seven years prior to

completion of the MDIP and the 14 years following. Cholera cases are assigned to the bari

location where they occurred, and the total cholera count for Matlab’s 7,490 baris is summed for

each of the two time periods, 1983-1989 and 1990-2003. From ICDDR,B demographic

surveillance we also calculate the mid-year bari population , and then sum the population counts

for each bari across the 1983-1989 and 1990-2003 time periods to create a total background

population at risk during each portion of the study period. Mid-year populations are appropriate

to use for longitudinal studies such as this, since they approximately balance out the number of

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births and deaths that a bari experiences during each year. Summing these annual mid-year

population counts also controls for the possibility of changing population sizes in baris across the

duration of the study period, such that population growth or decline at the bari level is factored

into individual baris’ cholera risk. A dichotomous variable (0 indicating 1983-1989 and 1

indicating 1990-2003) is assigned to differentiate between the bari-level cholera and population

counts for the pre- and post-flood protection period.

The original data set derived from ICDDR,B records had 14,980 entries: two for each of

7,490 baris, representing the cholera counts and population size before and after the flood control

embankment project. We then removed baris with zero population counts in either period. Zero

population records were more common in the first period because 1,609 baris were established

only after 1989. This elimination process yielded a rectangular data set with 5,390 baris in each

period.

The period cholera and population data for each bari are subsequently linked to a specific

geographic location in the Matlab GIS. The GIS is accurate within 10m and includes geographic

features such as bari locations, the Dhonagoda River, the MDIP embankment and the location of

the ICCDR,B hospital [2]. Using the GIS, each bari is assigned a flood protection status (1 for

protected or 0 for unprotected). All records for baris in the 1983-1989 period are given a 0 flood

protection status. Roughly one third of the 1990-2003 bari records are assigned a 1 flood

protection status, indicating that they are located within the protection of the MDIP embankment.

Two environmental variables have been shown to be correlated with cholera in Matlab:

distance to the ICDDR,B hospital and distance to the Dhonagoda River [2, 3, 12]. Straight line

Euclidean distance between each bari and the nearest portion of the river and the hospital is

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calculated using GIS tools. These two variables are then added to the suite of bari-level

information on cholera, population, period and flood protection status (Table 1).

Count data, such as the bari cholera counts examined in the present study, often are

characterized by overdispersion and excess zeros [15-17]. Zero-inflated (ZI) regression is a

practical way to model count data with both excess zeros and positive counts, as such models,

incorporating covariates, can be estimated simultaneously in the extra zeros and the count

distributional components of the model. Thus, ZI models are a highly useful approach to

providing a parsimonious specification for non-negative integer-valued data with extra zeros, but

only so when a key assumption underlying the models is plausible. These models assume that

the data are a mixture of two separate data-generating processes: one generates only zeros; the

other, usually a Poisson or negative binomial data-generating process, may also include zeros

along with non-zero integer counts. Thus, the data contain more zeros than expected under

standard Poisson, geometric or negative binomial distributions given the sample mean. Zero-

inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) dual-state regression models

have been widely applied in the social, economic, political and epidemiological sciences,

although caution is warranted when the strong assumption of zeros arising from two processes

cannot be sustained theoretically [18, 19].

Baris in the Matlab study area reporting zero cholera cases are viewed as consisting of

two subpopulations. The first subpopulation, producing only zeros, corresponds to baris that are

free of cholera due to a presumed combination of positive local environmental or infrastructure

factors (e.g., secure sanitary latrines, buried sewerage piping, uncontaminated ponds, and deep

protected tubewells). Zero cholera counts for these baris may be considered “true” zeros. The

second subpopulation consists of baris where cholera is actually prevalent but not reported,

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“false” zeroes. This situation can arise when an infected individual fails to seek medical

assistance because, for example, the infection is relatively mild or when self-treatment with oral

rehydration solution (ORS) is elected. A ZINB model can accommodate these excess “true” and

“false” zeros, and also overdispersion (extra heterogeneity) among the positive outcomes that

render a ZIP approach non-optimal. The parameter estimates in the count model, in our case a

negative binomial formulation, test for correlation between variables and increasing counts. The

zero-inflated parameter estimates, in contrast, represent correlation between the variables and a

zero count. Thus, the parameter estimates for the count model and the zero-inflated models are

typically of opposite signs.

The distribution of cholera counts in the Matlab region during the period of study is

overdispersed with respect to a Poisson distribution (empirical variance/mean = 2.881) and has

an excess of zeros (70.2% of observations), suggesting the appropriateness of a ZINB regression

model. The markedly skewed histogram in Figure 3 illustrates these features of the marginal

distribution. Several alternative models were specified and estimated, including classical

Poisson and negative binomial formulations, ZIP and ZINB models and so-called hurdle models

which allow the probability of observing a zero to be independent of the mean number of counts

but do not assume a dual-state data generating process [20]. Our final ZINB model (Table 2)

was selected on the basis of strong goodness of fit and conformity to our theoretical sense of the

underlying process generating the baris’ cholera counts. Parameter estimation in the ZINB

likelihood is carried out in R using the pscl package [21-24].

Results

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The results of fitting the ZINB regression model to the Matlab cholera counts using the

covariates discussed in Table 1 are shown in Table 2. Bari total population is included in the

model to account for background population risk. Figure 4 reveals the anticipated relationship

between cholera counts and population size, and this is reflected in the model parameter

estimates as well. Population has a strongly significant control effect in both the count and zero-

inflated part of the model. The very strong negative coefficient estimate in the ZI portion of the

model implies that the larger the bari’s population the lower the probability of it being cholera-

free.

Cholera incidence is directly related to the river distance variable in the count model net

of the other covariates. Cholera counts increase with increasing distance to the Dhonagoda. In

the zero-inflation portion of the model the positive coefficient suggests, however, that as distance

increases the frequency of zeros goes up, though this relationship is not statistically significant.

These results suggest that the influence of proximity to the Dhonagoda River has complex

interactions with cholera outcomes, as we explore in the following section.

The other distance variable in the model similarly behaves in an inconsistent fashion.

Cholera counts decline with increasing distance to the ICDDR,B regional hospital. The most

probable reason for this finding relates to difficulty of access, a consideration we develop more

fully in the following Discussion section. However, the zero-inflation portion of the model

further suggests that as distance to the regional hospital increases, the count of baris reporting no

cholera cases decreases.

The two key independent variables in this analysis provide the most interesting findings

from the study. Cholera counts in Matlab declined overall in the second portion of the study

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period and the frequency of zero reports increased, net of the other covariates, as evidenced by

the signs of the coefficients of the Period variable. We interpret this as a general decline in

cholera incidence in the region after 1990 (Figure 5) and develop this thought in our Discussion

section, below. What seems to be clear from the model is that this decrease following the

construction of the Meghna-Dhonagoda Irrigation Project in the late 1980s is not responsible for

the decline. Baris located within the flood controlled portion of our study area witnessed a

strong and significant increase in the reporting of cholera following the erection of the flood

control embankments and a positive flood protection status had no apparent influence on the

number of baris determined to be cholera-free.

Discussion

The background population of a bari is a large factor driving both cholera counts and the

division between baris with cholera and those without. The total population of a bari represents

the background risk, the number of opportunities for a cholera case to exist. Thus, as the

population of a bari increases the number of potentially infected individuals increases. Among

baris in the negative binomial count model, population is highly statistically significant and had

the largest coefficient. For baris that experienced cholera, higher numbers of residents acted as a

driver of higher cholera counts, there were more people be exposed and infected by the cholera

bacteria. Among baris with no cholera, population had a strong negative effect, with a

coefficient of -14.08, the largest in either model. As the population of a bari increases in the

zero-inflation model, the chance of baris remaining cholera-free greatly decreases. Among baris

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in Matlab, the total population of a residence has the largest effect on both any cholera cases

occurring and of higher numbers of cases.

The period variable (where 1 represents the 1990-2003 post-flood control period) was

significantly associated both with baris that experienced cholera during the study period and with

baris that did not, signaling a global decline of cholera in the study between the pre- and post-

flood control infrastructure (Figure 5). Among baris with zero cholera counts, a positive

association with period indicates that the 1990-2003 period is more strongly associated with an

absence of cholera in a bari than is the 1983-1989 period. Cholera in Matlab is decreasing as

general socioeconomic status improves, as access to clean water via tubewells increases, and as

availability and knowledge of prevention and treatment strategies spread [25].

Although travel to and treatment at the ICDDR,B hospital is free for Matlab’s residents,

there still exists a distance decay effect across baris. Residents who live further away from the

hospital, which is located in the southwestern portion of the study area (Figure 2), appear to be

less likely to regularly report to the hospital and have cholera diagnosed. This distance effect is

clearly seen in the negative relationship with hospital distance in the negative binomial count

model, where baris distant from the hospital do experience cholera counts but in lower numbers

than baris close to the hospital. Paradoxically, however, the weaker (negative) relationship in the

ZI portion of the model suggests that as hospital distance increases the number of baris reported

as cholera-free declines. While explanations for this relationship remain unclear, it might be due

to underlying spatial patterns of unmeasured variables such as differing perceptions of risk

associated with non-treatment of cholera-like symptoms or preference for self-medication with

ORS.

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The relationship between cholera and proximity to the Dhonagoda River is similarly

paradoxical. Baris that are further from the river either reported more cholera cases or more

frequently reported zero cholera. We had hypothesized that there would be a negative

relationship between cholera and river proximity, believing that the flooding of the Dhonagoda

River constituted a primary source of potentially cholera-contaminated water. Perhaps, however,

the opposite is true, that baris distant from the river are more dependent on stagnant or backwater

sources of drinking, cooking and bathing water, sources that might have higher levels of bacterial

contamination. The river also acts as a primary transportation route through Matlab, so it could

be that baris further from the river are less likely to travel to the hospital, and thus more

frequently report zero cholera. While we are unsure of the precise relationship that our model

indicates, it is clear that the Dhonagoda River has complex and spatially diverse effects on

cholera outcomes.

Residence in the flood protected area of Matlab, when all the other environmental

variables are controlled for, has a statistically significant positive effect in the cholera count

model. It has no effect in the zero-inflation model. Thus, while the implementation of flood

protection appears to have had no effect on whether a bari experiences cholera, it does act to

increase the number of cholera cases among baris with cholera. While the positive relationship

between flood protection and cholera may seem counterintuitive, it helps to think of monsoon

flooding as a natural part of the aquatic cycle in Matlab. Monsoon flood waters act as a system

reset, flushing out depleted and potentially cholera infected water supplies. We suggest that

baris protected from this flooding have greater continued exposure to cholera bacteria in the

environment, either through natural occurrence or through contamination of water supplies by

human waste. Alternately, rather than an environmental explanation, we conjecture that there

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could be a behavioral change responsible for the relationship between flood protection and

increased cholera counts: if people believe themselves to be better-protected from choleric water

supplies they could relax their guard against interacting with contaminated water.

The process by which an individual resident of Matlab is exposed to and becomes

infected with the cholera bacterium is dependent on the dynamic interactions of a wide array of

population and environmental factors. Whether that individual goes on to infect others is further

dependent on the timing and occurrence of these variables. While we have examined only a few

of the many factors believed to be important to cholera outcomes, it is useful to examine the

broad patterns by which the residential environment of Matlab contributes both to the presence

of cholera in a bari and to the propagation of the disease among certain baris over time. Our

results illustrate that many factors important to the degree to which a bari experiences cholera are

also important in determining whether a bari experiences cholera at all. The alteration of

Matlab’s traditional aquatic cycle for a portion of the study population via the construction of the

MDIP embankment, however, appears to act as a driver of higher cholera counts, and does not

confer any significant protection against a bari ever experiencing cholera.

Conclusions

Ongoing construction of flood protection structures in Bangladesh, and the continued

alteration of water ecosystems for economic development in other countries, will likely continue

to have adverse effects on human health until these mechanisms are better understood. While

those in favor of water management schemes can list increased agricultural productivity and

other benefits, the fact remains that the planning, implementation and monitoring stages of such

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projects need to explicitly account for increased occurrence of endemic waterborne diseases.

Our longitudinal analysis of highly detailed and rigorously collected health data confirms

previous studies that the introduction of flood protection in Matlab amplified cholera occurrence,

even as the overall incidence of cholera in Matlab was on the decline. These unintended “side

effects” must be considered by health officials in Matlab and elsewhere as water systems are

modified. Such considerations, when jointly made by environmental, agricultural, development

and public health officials, should help public agencies work together meet mutual goals, among

them direct public health mitigation efforts.

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List of Abbreviations

FP Flood Protection

GIS Geographic Information System

ICDDR, B International Centre for Diarrhoeal Disease Research, Bangladesh

MDIP Meghna-Dhonagoda Irrigation Project

NGO Non-Governmental Organization

ORS Oral Rehydration Solution

ZI Zero-Inflated

ZINB Zero-Inflated Negative Binomial

ZIP Zero-Inflated Poisson

Competing Interests

The authors declare they have no competing interests.

Authors’ Contributions

MC conceived of the study, carried out the data preparation, participated in statistical analysis

and drafted the manuscript. PV conducted statistical analysis and helped to draft the manuscript.

PKS and MY oversaw the design and collection of the dataset and helped interpret findings in

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the context of the study area. ME conceived of the study and participated in its design and

coordination and helped draft the manuscript. All authors read and approved the final

manuscript.

Acknowledgements

This research was supported through grants from the NOAA Oceans and Human Health

Program, the joint NSF-NIH Ecology of Infectious Diseases Initiative (Grant # R01 TW008066-

03), the NSF Graduate Research Fellowship Program, and the NSF IGERT Program at the

Carolina Population Center at the University of North Carolina at Chapel Hill. Cholera case data

and demographic data used for this research was funded by ICDDR, B and donors who provide

unrestricted support to ICDDR, B for its operation and research. Current donors providing

unrestricted support include: Australian Agency for International Development (AusAID),

Government of the People's Republic of Bangladesh, Canadian International Development

Agency (CIDA), Embassy of the Kingdom of the Netherlands (EKN), Swedish International

Development Cooperation Agency (Sida), Swiss Agency for Development and Cooperation

(SDC), and Department for International Development, UK (DFID). We gratefully acknowledge

these donors for their support and commitment to the Centre's research efforts.

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Figure Legends

Figure 1: View of the MDIP embankment from a bari located inside of the flood protected area.

Figure 2: Map of the main geographic features of Matlab, Bangladesh. Baris protected from

flooding by the MDIP embankment are darkened circles, unprotected baris are hollow.

Figure 3: Frequency distribution of the number of cases of cholera reported by individual baris in

Matlab, 1983-2003.

Figure 4: Frequency distribution of cholera counts by bari population. Baris with no population

in either period have been removed from the analysis leaving a final N = 11,780 (5,390 baris,

each represented twice in this graph).

Figure 5: Cholera counts in Matlab, Bangladesh from 1983-2003. Cases are assigned to flood

protection status based on bari of incidence. Cases taking place prior to 1990 are given the flood

protection status of the bari following MDIP embankment construction.

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Tables

Table 1: Model variables and their anticipated relationship to cholera prevalence.

Model Variables Measure Hypothesized Relationship

Period 1 (1983-1989)/ 0 (1990-2003) Negative (due to overall decline in cholera incidence)

Background Population Total count per period/1000 Positive (higher population increases cholera risk)

Flood Protection Status 1 (Protected)/ 0 (Unprotected) Positive (being flood protected increases risk)

Distance to River Euclidean distance (km)

Negative (due to decreased risk of flooding further from

river)

Distance to Hospital Euclidean distance (km) Negative (due to distance decay of traveling to hospital)

Outcome Variable

Cholera Prevalence Total count per period

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Table 2: Maximum likelihood parameter estimates of the multiple ZINB regression model.

Negative Binomial Model Zero-Inflated Model

Parameter Estimate S.E. 95% CI Estimate S.E. 95% CI

Intercept 0.476 0.050 0.377 0.574 *** 1.708 0.128 1.458 1.958 ***

Period (0, 1) -0.315 0.045 -0.403 -0.227 *** 0.891 0.158 0.582 1.200 ***

FP status (0, 1) 0.535 0.047 0.442 0.628 *** -0.158 0.224 -0.598 0.281

River distance 0.064 0.018 0.030 0.099 *** 0.0990 0.071 -0.048 0.229

Hospital distance -0.222 0.007 -0.236 -0.209 *** -0.069 0.034 -0.137 -0.002 *

Population (1,000) 1.284 0.056 1.174 1.395 *** -13.029 0.962 -14.915 -11.143 ***

log(theta) 0.418 0.059 0.302 0.534 ***

Significance values: 0 '***' 0.001 "**' 0.01 '*' 0.05 ' '

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Figure 1

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